Subgroups — #25097165

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
2	#19137200	C₂	1	2	yes	maximal
3	#19134758	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134753	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134727	C₂	1	2	yes	maximal, complemented
6	#19134627	C₂	1	2	yes	maximal
7	#19134621	C₂	1	1	yes	maximal, characteristic
8	#19134621	C₂	1	1	yes	maximal, characteristic
9	#19134493	C₂	1	2	yes	maximal, complemented
10	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
14	C₂×#13063282	C₂²	1	1	yes	characteristic
15	C₂×#13063259	C₂²	1	1	yes	characteristic
16	C₂×#13063259	C₂²	1	1	yes	characteristic
17	C₂×#13063258	C₂²	1	2	yes	—
18	C₂×#13063256	C₂²	1	2	yes	—
19	#14582853	C₄	1	8	yes	complemented
20	C₂×#13063236	C₂²	1	1	yes	characteristic
21	C₂×#13063235	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
23	#14582790	—	2	2	no	—
24	#14582788	—	2	2	no	—
25	#14582783	—	2	2	no	—
26	#14582781	—	2	2	no	—
27	#14582768	C₂²	1	2	yes	—
28	#14582764	C₂²	1	2	yes	—
29	#14582756	C₂²	1	2	yes	—
30	#14582756	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582661	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
41	C₂×#10621872	—	2	2	no	—
42	C₂×#10621872	—	2	2	no	—
43	C₂×#10621872	C₂×C₄	1	4	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₈×D₄₃	—	2	2	no	—
47	C₂×C₈×D₄₃	—	2	2	no	—
48	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
49	#13063282	C₂×C₄	1	4	yes	—
50	#13063282	Q₈	1	4	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×Dic₄₃⋊C₄	—	2	2	no	—
54	C₂×Dic₄₃⋊C₄	—	2	2	no	—
55	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
56	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
60	C₂×(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
63	#13063259	—	2	2	no	—
64	#13063259	—	2	2	no	—
65	#13063258	—	2	4	no	—
66	#13063256	—	2	4	no	—
67	#13063236	C₂×C₄	1	4	yes	—
68	#13063235	C₂×C₄	1	4	yes	—
69	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₄₃⋊#95	—	2	2	no	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₃	—	2	2	no	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	2	no	—
82	#107×C₄₃	—	2	2	no	—
83	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
84	#95×C₄₃	—	2	2	no	—
85	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₃	—	2	2	no	—
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
98	C₂×C₄×D₄₃	—	2	1	no	—
99	C₂×C₄×D₄₃	—	2	1	no	—
100	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	—	2	1	no	—
104	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₃	#41	1	2	yes	—
107	C₂×C₈×C₄₃	#41	1	2	yes	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄²×C₄₃	—	8	2	no	—
113	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
115	(C₂×D₄₃)⋊C₄	—	8	2	no	—
116	(C₂×D₄₃)⋊C₄	—	8	2	no	—
117	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	4	yes	—
118	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	4	yes	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	Dic₄₃⋊C₄	—	8	2	no	—
124	Dic₄₃⋊C₄	—	8	2	no	—
125	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
126	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
127	C₄×Dic₄₃	—	8	2	no	—
128	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
130	C₂×C₄₃⋊C₈	—	2	1	no	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₃⋊C₈	#41	1	2	yes	—
135	C₂×C₄₃⋊C₈	#41	1	2	yes	—
136	#10621872	—	2	8	no	—
137	C₈×D₄₃	—	2	8	no	—
138	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	C₂²×D₄₃	—	2	1	no	—
140	C₂²×D₄₃	—	2	1	no	—
141	C₂²×D₄₃	—	2	1	no	—
142	C₂²×D₄₃	—	2	1	no	—
143	C₂²×D₄₃	—	2	1	no	—
144	C₂²×D₄₃	—	2	1	no	—
145	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	1	no	—
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₄×D₄₃	—	2	2	no	—
180	C₄×D₄₃	—	2	2	no	—
181	C₄×D₄₃	—	2	2	no	—
182	C₄×D₄₃	—	2	2	no	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	#117	1	4	yes	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	#117	1	4	yes	—
187	#20821	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×C₄₃	#532	1	1	yes	characteristic
190	C₂²×C₄₃	#532	1	1	yes	characteristic
191	C₂²×C₄₃	#576	1	1	yes	characteristic
192	C₂²×C₄₃	#576	1	1	yes	characteristic
193	C₂²×C₄₃	#578	1	1	yes	characteristic
194	C₂²×C₄₃	#578	1	1	yes	characteristic
195	C₂×D₄₃	—	2	2	no	—
196	C₂×D₄₃	—	2	2	no	—
197	C₂×D₄₃	—	2	2	no	—
198	C₂×D₄₃	—	4	1	no	—
199	C₂×D₄₃	—	4	1	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	4	1	no	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	—	8	2	no	—
206	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
207	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
208	C₄×C₄₃	#533	1	1	yes	characteristic
209	C₄×C₄₃	#533	1	1	yes	characteristic
210	Dic₄₃	—	2	2	no	—
211	Dic₄₃	—	2	2	no	—
212	Dic₄₃	—	2	2	no	—
213	Dic₄₃	—	8	2	no	—
214	Dic₄₃	—	8	2	no	—
215	C₂×#405	—	43	1	no	—
216	#2314	—	43	2	no	—
217	#1846	—	43	1	no	—
218	#1845	—	43	1	no	—
219	#1836	—	43	2	no	—
220	#1809	—	43	2	no	—
221	#1808	—	43	1	no	—
222	#1808	—	43	1	no	—
223	#1776	—	43	2	no	—
224	C₄×#107	—	43	1	no	—
225	C₄×#107	D₄₃	1	1	yes	characteristic, complemented
226	C₂×C₄₃	#2285	1	1	yes	characteristic
227	C₂×C₄₃	#2913	1	1	yes	characteristic
228	C₂×C₄₃	#2913	1	1	yes	characteristic
229	C₂×C₄₃	#3175	1	1	yes	characteristic
230	C₂×C₄₃	#3175	1	1	yes	characteristic
231	C₂×C₄₃	#3176	1	1	yes	characteristic
232	C₂×C₄₃	#3177	1	1	yes	characteristic
233	D₄₃	—	4	2	no	—
234	C₂²×M₁₆	—	43	1	no	—
235	C₂³×C₈	—	43	1	no	—
236	C₂×#117	—	43	1	no	—
237	C₂×#107	—	43	1	no	—
238	C₂×#107	—	43	1	no	—
239	C₂×#107	—	43	2	no	—
240	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
241	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
242	C₂×#106	—	43	2	no	—
243	#405	—	43	8	no	—
244	C₂×#97	—	43	1	no	—
245	C₂×#97	—	43	1	no	—
246	C₂×C₄×C₈	—	43	1	no	—
247	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
248	#388	—	86	2	no	—
249	#388	—	86	2	no	—
250	#387	—	86	2	no	—
251	#387	—	86	2	no	—
252	#384	—	43	2	no	—
253	#382	—	43	2	no	—
254	#380	—	43	2	no	—
255	#380	—	43	2	no	—
256	C₄×C₄⋊C₄	—	43	2	no	—
257	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
258	#340	—	43	2	no	—
259	#340	—	43	2	no	—
260	#340	—	43	2	no	—
261	#340	C₂×D₄₃	1	2	yes	—
262	C₄₃	#20821	1	1	yes	characteristic, complemented, Sylow
263	C₂³×C₄	—	43	1	no	—
264	C₂×M₁₆	—	43	4	no	—
265	C₂×M₁₆	—	86	2	no	—
266	C₂×M₁₆	—	86	2	no	—
267	C₂²×C₈	—	43	1	no	—
268	C₂²×C₈	—	43	1	no	—
269	C₂²×C₈	—	43	4	no	—
270	C₂²×C₈	—	86	2	no	—
271	C₂²×C₈	—	86	2	no	—
272	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
274	#117	—	43	4	no	—
275	#117	—	43	4	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	43	1	no	—
278	C₂×C₄⋊C₄	—	43	2	no	—
279	C₂×C₄⋊C₄	—	43	2	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₄⋊C₄	—	86	2	no	—
282	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
284	C₂×C₂²⋊C₄	—	43	1	no	—
285	C₂×C₂²⋊C₄	—	43	1	no	—
286	C₂×C₂²⋊C₄	—	86	2	no	—
287	C₂×C₂²⋊C₄	—	86	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	43	1	no	—
290	C₂×C₄²	—	86	2	no	—
291	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	86	4	no	—
295	#107	—	86	2	no	—
296	#107	—	86	2	no	—
297	#106	—	86	4	no	—
298	#97	—	43	4	no	—
299	#97	—	43	4	no	—
300	C₄×C₈	—	43	4	no	—
301	C₄×C₈	C₄×D₄₃	1	4	yes	—
302	#95	—	2	2	no	—
303	#95	—	86	2	no	—
304	#95	—	86	2	no	—
305	#95	—	86	2	no	—
306	#95	—	86	2	no	—
307	#95	—	86	2	no	—
308	C₂⁴	—	43	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	43	1	no	—
312	C₂²×C₄	—	43	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	43	2	no	—
315	C₂²×C₄	—	43	2	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	1	no	—
319	C₂²×C₄	—	86	1	no	—
320	C₂²×C₄	—	86	2	no	—
321	C₂²×C₄	—	86	2	no	—
322	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
324	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
325	M₁₆	—	86	8	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	43	2	no	—
329	C₂×C₈	—	43	2	no	—
330	C₂×C₈	—	43	2	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	8	no	—
335	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
337	C₂×C₈	#10621898	1	2	yes	—
338	C₂×C₈	#10621898	1	2	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	43	4	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	344	2	no	—
350	C₄⋊C₄	—	344	2	no	—
351	C₂²⋊C₄	—	43	4	no	—
352	C₂²⋊C₄	—	43	4	no	—
353	C₂²⋊C₄	—	344	2	no	—
354	C₂²⋊C₄	—	344	2	no	—
355	C₄²	—	8	2	no	—
356	C₄²	—	43	2	no	—
357	C₄²	—	43	2	no	—
358	C₄²	—	344	2	no	—
359	C₄²	C₂×C₄×D₄₃	1	2	yes	—
360	C₄²	Q₈×D₄₃	1	2	yes	—
361	C₂³	—	43	2	no	—
362	C₂³	—	86	1	no	—
363	C₂³	—	86	1	no	—
364	C₂³	—	86	1	no	—
365	C₂³	—	86	1	no	—
366	C₂³	—	86	1	no	—
367	C₂³	—	86	1	no	—
368	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	43	2	no	—
380	C₂×C₄	—	43	2	no	—
381	C₂×C₄	—	43	2	no	—
382	C₂×C₄	—	86	1	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	1	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	86	2	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	86	2	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	—	172	2	no	—
394	C₂×C₄	—	172	2	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
399	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
400	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
402	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
403	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	43	4	no	—
408	C₈	—	86	2	no	—
409	C₈	#13063282	1	4	yes	—
410	C₂²	—	86	2	no	—
411	C₂²	—	86	2	no	—
412	C₂²	—	86	2	no	—
413	C₂²	—	172	1	no	—
414	C₂²	—	172	1	no	—
415	C₂²	—	172	1	no	—
416	C₂²	—	172	1	no	—
417	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
418	C₂²	#14583446	1	1	yes	characteristic
419	C₂²	#14583446	1	1	yes	characteristic
420	C₂²	#14583700	1	1	yes	characteristic
421	C₂²	#14583701	1	1	yes	characteristic
422	C₂²	#14583712	1	1	yes	characteristic
423	C₂²	#14583713	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	86	2	no	—
429	C₄	—	86	2	no	—
430	C₄	—	86	2	no	—
431	C₄	—	344	2	no	—
432	C₄	—	344	2	no	—
433	C₄	#117×D₄₃	1	1	yes	characteristic
434	C₄	C₂×#13063282	1	1	yes	characteristic
435	C₄	#14583453	1	1	yes	characteristic
436	C₄	#14583453	1	1	yes	characteristic
437	C₂	—	172	2	no	—
438	C₂	#19136999	1	1	yes	characteristic
439	C₂	#19143191	1	1	yes	characteristic
440	C₂	#19143192	1	1	yes	characteristic
441	C₂	#19145230	1	1	yes	characteristic
442	C₂	#19145236	1	1	yes	characteristic
443	C₂	#19145241	1	1	yes	characteristic
444	C₂	#19145250	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#107×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#107	D₄₃
hypocenter	C₄₃	#20821
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #19134758	C₂	semidirect
4. #19134753	C₂	semidirect
5. #19134727	C₂	semidirect
9. #19134493	C₂	semidirect
10. C₄×#13063259	C₂	semidirect
11. C₄×#107×C₄₃	C₂	semidirect
19. #14582853	C₄	semidirect
225. C₄×#107	D₄₃	semidirect
262. C₄₃	#20821	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14582853	2
#19137200	2
#19134758	2
#19134753	2
#19134727	2
#19134627	2
#19134621	2
#19134493	2
C₄×#13063259	2
C₄×#107×C₄₃	2
#20821	43